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Experimental investigation of residual stresses in steel cellular and castellated members
Construction and Building Materials 54 (2014) 512–519
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Experimental investigation of residual stresses in steel cellular and castellated members Delphine Sonck ⇑, Rudy Van Impe, Jan Belis Department of Structural Engineering – LMO, Ghent University, Technologiepark-Zwijnaarde 904, 9052 Ghent, Belgium
h i g h l i g h t s Cellular or castellated members are fabricated from hot-rolled parent sections. Residual stresses lower the global buckling resistance of the parent sections. The production process influence was determined by measuring the residual stress. During the production process, the residual stresses become more detrimental.
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Article history: Received 26 August 2013 Received in revised form 29 November 2013 Accepted 16 December 2013 Available online 23 January 2014 Keywords: Residual stresses Cellular members Castellated members Hot-rolled I-members Imperfection Flexural buckling Lateral–torsional buckling
a b s t r a c t The global buckling resistance of hot-rolled steel I-section members is adversely influenced by the presence of residual stresses. It is expected that thermal effects during the production of cellular and castellated members will influence the already present stresses in the hot-rolled parent sections, but it is yet unknown to what extent. In this paper, the experimental investigation of the residual stresses in these members is described, and it is shown that the production process increases the already present compressive flange stresses, which will be detrimental for their buckling resistance. This effect will be even more pronounced for deviating production procedures. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Cellular or castellated members are I-section members with circular or hexagonal web openings regularly spaced along the length of the member. Usually, they are manufactured starting from steel hot-rolled I-section members of which the web is thermally cut according to a certain pattern, after which the obtained halves are shifted and rewelded (Fig. 1). Variations in the cutting pattern and the properties of the top and bottom halves of the beam result in a large variety of final member geometries, in which tapered beams, different web opening shapes or asymmetric beams are possible. The main advantage of cellular or castellated members compared to normal I-section members is their increased strong-axis bending resistance. Furthermore, service ducts can be guided
⇑ Corresponding author. Tel.: +32 9 2645469. E-mail addresses: [email protected] (D. Sonck), Rudy.VanImpe@ UGent.be (R. Van Impe), [email protected] (J. Belis). 0950-0618/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2013.12.045
through the web openings instead of under the member, thus diminishing the necessary total story height. Additionally, they can also be used out of aesthetic considerations because of their lighter appearance. The members are mainly used for applications in which they are loaded in bending, both in steel and steel– concrete construction. However, they are also increasingly used for columns and beam-columns, where the column is subjected to both bending and compression. Clearly the presence of the web openings will influence the failure behaviour of cellular or castellated members [1]. For instance, new localized failure modes can arise, such as Vierendeel bending around the web openings or local buckling of the web surrounding the openings. Specific rules for these failure modes are currently being developed and optimized [2–8]. However, the already existing failure modes for I-section members will also be modified, because of the change in geometry and the influence of the production process on imperfections such as geometric imperfections and residual stresses. Examples of this are the global instability failure modes for members loaded in compression and/or bending, such as
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Fig. 1. Standard fabrication method of castellated and cellular members starting from a plain-webbed parent section.
flexural buckling or lateral–torsional buckling. Unfortunately, the existing research for these global instability modes is incomplete, conflicting or lacking altogether [9–11]. An important aspect of the global instability behaviour of cellular and castellated members that has not been investigated yet is the influence of residual stresses. Residual stresses are internal stresses which can exist in a member not subjected to external loads. Hence, residual stresses are always in static equilibrium. In hot-rolled I-section members, thermal residual stresses originate during the cooling after the hot-rolling process because of the non-uniform cooling and corresponding thermal contraction, coupled with a temperature-dependent yield stress. Typically, the flange tips will be in compression and the flange centres in tension, while the sign and variation of the residual stresses in the web varies depending on the cooling parameters and cross-section geometry [12–17]. Examples of typical thermal residual stress shapes are shown in Fig. 2 [17,18]. If the straightness of the beams after cooling is not sufficient, the beams will undergo a cold-straightening process which redistributes the residual stresses in the flanges [19,20]. As a result, the possible residual stress patterns in I-section members are very diverse. The influence of residual stresses on the global buckling failure of I-section members without web openings has been studied extensively for the cases of flexural buckling [14,15] and lateral– torsional buckling [21], which are the most important global failure modes for I-section members. It was shown that the residual stresses have a detrimental effect on the global buckling resistance of the I-section members, caused by the compressive residual stresses at the flange tips. Due to these stresses, the onset of yielding will occur quicker at the flange tips, increasing the members’ flexibility and reducing the corresponding buckling resistance. Furthermore, it was shown that the redistribution of the flange stresses due to cold-straightening is always advantageous for the failure load [16,19,20,22]. Therefore, it was decided not to take this into account in the proposed standard residual stress patterns and to consider only the more detrimental thermal residual stress pattern in finite element calculations to determine the buckling resistance. Likewise, only non-straightened members were used in the flexural buckling experiments to determine the buckling resistance of columns [23]. During the cutting and welding processes in the production of cellular or castellated members, heat is introduced at the cutting
(a)
and welding locations, which will influence the already present residual stresses. At the locally heated zone, very high tensile residual stresses (up to the material’s yield stress) will be present, balanced by compressive (and possibly also tensile) stresses farther away from the location of heat introduction [15,19,23–28]. Typical schematized residual stress distributions for plates cut at one side and plates welded in their middle are depicted in Fig. 3. As a result, it is very well possible that the production process increases the magnitude of the compressive residual stresses in the flanges, hence decreasing the global buckling failure load. Nevertheless, the change in residual stresses of cellular and castellated members during their production process has not been investigated yet and it is currently not known how significant the possible detrimental effect on the members’ stability will be. In this paper, the effect of the production process of cellular and castellated beams on the residual stresses is investigated by measuring the residual stresses in a series of castellated and cellular members. Measurements were done both for the parent sections and the resulting castellated and cellular members. By comparing the measured stresses before, during, and after production, the effect of the production procedure could be studied. In this paper, tensile stresses will be taken as positive stresses and compressive stresses as negative. 2. Residual stress measurement method and specimens In this section, an overview will be given of the used measurement method and the specimens in which the residual stresses were measured. All measurements were done at the Laboratory for Research on Structural Models (LMO, Ghent University). 2.1. Measurement method The residual stresses were measured using the sectioning method, which is a destructive relaxation method. The longitudinal residual stresses in each segment can be calculated using the strain difference before and after the relaxation of each segment. The relaxation of each segment is accomplished by the sectioning of the member. First, the member is cut transversally at the location of measurement, after which a series of longitudinal cuts is made to separate all segments in which the strains are measured
(b)
Fig. 2. Residual stress pattern in hot-rolled I-section members: (a) according to ECCS [18]; (b) according to Young [17].
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(a)
(b)
Fig. 3. Schematized residual stress pattern in: (a) plate welded in middle; (b) plate cut at one end.
were permanently damaged during the measurements: from the total of 360 used strain gages, 31 were found faulty. The measured strains in these gages (if any) were not included in the results. 2.2. Used specimens
Fig. 4. Overview of the sectioning method.
(Fig. 4). Because of its straightforwardness, this method is the primary method for the longitudinal residual stress measurement in steel I-section members, having been extensively used in the past as well as nowadays [12–15,17,20,22,24–29]. At each measurement location, the residual stress magnitude rres was calculated according to Eq. (1) using the measured relaxation strains emeas and the modulus of elasticity E. It was assumed that the specimens behaved elastically during the measurements, that the transverse residual stresses could be neglected, and that the thermal influence of the cutting process on the residual stresses was negligible.
rres ¼ E emeas
ð1Þ
The residual stresses were expected to vary along the length of the non-uniform castellated and cellular members. To study this effect, the residual stresses in these members were measured between the openings (web post in Fig. 1) and at the centre of an opening (tee section in Fig. 1). Adhesively bonded electrical strain gages were used to cope with the necessary short gage length. Another advantage of using electrical gages was that the strain variation during the measurement (and cutting) process could be easily monitored continuously. The resistance changes corresponding with the strain variations in the strain gages were measured using a Wheatstone bridge. Temperature variations during the sectioning process were accounted for by using self-temperature-compensated strain gages specifically designed for mild steel. The error on the strain measurement is estimated to be ±1.5%. The cutting process was executed with an electrical band saw, combined with a handsaw for some of the transverse cuts. Cutting oil was used to limit local heating of the specimens. A protective coating was used to protect the strain gages from this oil. During the cutting, the measured strains were continuously monitored to be sure that there was no malfunctioning of the strain gages due to damage suffered during the multiple manipulations throughout the sectioning process. However, some strain gages
Four castellated and two cellular members were made starting from six IPE160 parent sections: three geometries were used and two members were made for each geometry. Geometries CS1 and CS3 had hexagonal openings, while the CS2 beams had circular openings (Fig. 5). The steel grade of the members was S275, with a nominal yield stress of 275 MPa. Tensile tests to determine the yield stress fy were executed on specimens from the flanges and the web of each member (Table 1). The Young’s modulus E could also be derived from the tensile test measurements. Unfortunately, some of the obtained values for E were too aberrant from the mean values given in literature [30], probably due to a faulty displacement measurement during the test (these values are not included in Table 1). As a result, it was chosen not to use the measured values of E for the residual stress calculations, but to use E = 210 GPa as a safe mean value. Taking the variability of the values of the Young’s modulus E into account, the possible error on the residual stress measurements increases. This can be illustrated for the flange stresses, using values of Emean ± 2 Est. dev., based on the measured values of E in the flanges. If the real value of E would be 179 GPa instead of the used 210 GPa, the calculated residual stress is 15% larger than its real value. On the other hand, if E = 223 GPa, the calculated residual stress is 6% smaller than the real residual stress value. Six IPE160 beams of 12 m long were used as the parent section. Before the production of the castellated and cellular members, a specimen of 1 m long was cut from each parent section beam, to determine the original residual stress pattern in the parent sections. Geometries CS1 and CS3 were made following the standard
Table 1 Yield stresses obtained from the tensile tests, comparison with literature [30]. Yield stress, fy [MPa]
Web Flanges Literature
Young’s modulus, E [GPa]
# Samples
fy,mean
fy,st.
8 12 –
332 346 327.93
7 5 18.96
dev.
# Samples
Emean
Est.
6 11 –
195 201 205.47
12 11 13.18
Fig. 5. Dimensions [mm] of the parent section PS and the castellated and cellular member geometries CS .
dev.
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Fig. 6. Production process: (a) cutting of the web; (b) welding of the castellated members; (c) additional cutting of the circular openings for the CS2 geometries.
procedure depicted in Figs. 1 and 6a and b. First, the parent section webs were cut according to the corresponding pattern for hexagonal openings using an oxyfuel cutting process. After the cutting of the web, both halves of the beam were shifted and welded together again using a semiautomatic MAG welding process. A but joint existing of two weld passes – one on each side of the web – was used. For each of both geometries, a section was left unwelded so that the influence of the cutting process alone on the residual stresses could be studied in the obtained castellated member halves. The CS2 geometries had circular openings. Normally, cellular members are fabricated following a similar procedure as for castellated members, with two cut lines in the web instead of one to obtain the circular opening shapes (Fig. 1). However, the production of the two CS2 members deviated from this procedure: the members were made by cutting circular openings around the hexagonal openings of two completed castellated members with a CS1 geometry (Fig. 6c). Thus, the effect of deviating production procedures on the residual stresses could be examined as well. The heat input using this deviating procedure was larger than for the standard production procedure of CS1 and CS3 because the cutting process had to be restarted for each separate web opening. The strains were measured at five locations in each flange. In the web, five strain gages were used for the parent sections, while two gages were used at the tee section and eight at the web post for the cellular or castellated members. It was expected that measurements on one side of the flanges or the web would suffice, since it had been shown that the through-thickness stress variations in thin-walled hot-rolled members such as the considered specimens is limited [12,13]. Consequently, all measurements were done on the outer side of the flanges and on the same side of the web. The exact location of the strain gages is given in Appendix A. An overview of the specimens in which the residual stresses were measured is given in Table 2. In total, the residual stresses were measured in six parent section specimens (PS), two unwelded castellated member specimens (AC) and seven castellated or cellular member specimens (AW). For both the AC and AW specimen types, measurements were made at two locations along the
length: the residual stresses were determined between two openings (web post WP) and at the centre of an opening (tee section TS). The measurements in the unwelded castellated members specimens occurred for both the top and bottom halves of the cut IPE160 section. All specimens were taken from the same end of the members. The length of each specimen was chosen such that the distance between the measurement locations and the specimen edge was at least twice the height of the specimen. Thus, possible disturbances of the residual stresses by edge effects were avoided. The remainder of the castellated and cellular members is being used for buckling experiments which are beyond the scope of this contribution. 3. Measurement results and discussion 3.1. Measurement results The results of the residual stress measurements in the parent section are shown in Fig. 7. The effect of the cutting of the parent sections of the CS1 and CS3 geometries can be seen in Fig. 8, both for the tee section and the web post. The final residual stress distribution in the geometries CS1 and CS3 is shown in Fig. 9, while the residual stress distribution for CS2 is shown in Fig. 10. The measurements for geometries CS1 and CS3 are shown together, since they were found to be very similar. In Figs. 7–9, the measured values of the residual stresses are shown for each specimen, together with the corresponding leastsquare fit (LSF) curves for the residual stresses in the flanges. The LSF curves were obtained by mirroring the results about the horizontal and vertical symmetry axes of the cross-section, after which these values were fitted to a linear function. This function shape is based on the perceived variation of the residual stresses across the flanges. Since the compressive residual flange stresses have a dominant detrimental influence on the global buckling resistance, an overview of the variation of the flange stresses during the production process is depicted in Fig. 11. Here, the least-square fit curves of the measured residual stresses in the flanges are shown. 3.2. Discussion of residual stress measurements
Table 2 An overview of the test specimens. Measurements were done in three different sections: parent section (PS), sections after cutting (AC) and after welding (AW). In the latter two, measurement occurred at the web post between two openings (WP) and at the tee section at an opening (TS). Member name
# Locations parent section (PS)
# Locations after cutting (AC)
# Locations after welding (AW)
CS1L1 CS1L2 CS2L1 CS2L2 CS3L1 CS3L2
PS
WP
TS
WP
TS
1 1 1 1 1 1
2 0.5 0 0 0 2 0.5 0
2 0.5 0 0 0 2 0.5 0
1 1 2 1 1 1
1 1 2 1 1 1
Total
6
2
2
7
7
3.2.1. Influence of cold-straightening It was expected that the plastic deformation corresponding with the cold-straightening of a member around its weak axis is perceivable through antisymmetric residual stress deviations in the flanges. In the parent sections (Fig. 7), no influence of the cold-straightening of the beam was observed in the measured residual stresses in the flanges. However, in the flanges of the AC and AW specimens, the influence of cold straightening on the residual flange stresses is visible (Figs. 8–10). 3.2.2. Parent sections (PS) The measured residual stresses in the parent section (Fig. 7) are consistent with earlier results from literature and lie between the
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(a)
(b)
Fig. 7. Measured residual stresses in the parent section PS (a); comparison of the measured PS residual stresses with results from literature (b).
(a)
(b)
Fig. 8. Measured residual stresses in CS1 and CS3 in both halves after the cutting of the web during production: (a) in the web post; (b) in the tee section.
residual stress patterns proposed by Young and the ECCS [17,18], shown in Fig. 7. Furthermore, it can be seen that the measured residual stresses were very similar for the six parent section specimens, suggesting that all parent sections came from the same batch. 3.2.3. Member halves after cutting of the parent sections (AC) In Figs. 8 and 11, the residual stresses in the parent section halves obtained after the oxycutting of the web are depicted. It
was expected that this cutting of the parent sections would have a dual influence on the stresses in the obtained halves. Firstly, the thermal influence of the cutting process will induce tensile stresses at the cut, balanced by both compressive and tensile stresses further away from the cut. Secondly, an elastic rebound of the isolated halve of the member will occur when the forces acting on it by the other halve are removed. For the considered specimens, the elastic rearrangement of the residual stresses due to the elastic rebound was expected to increase the compressive flange stresses.
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(a)
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(b)
Fig. 9. Measured residual stresses in completed CS1 and CS3: (a) in the web post; (b) in the tee section.
(a)
(b)
Fig. 10. Measured residual stresses in completed CS2: (a) in the web post; (b) in the tee section.
However, this compressive stress increase was expected to be counteracted by the increase in tensile flange stresses due to thermal effects. The total influence of the oxycutting process on the flange residual stresses in the beam halves was seen to be rather limited (Figs. 8 and 11). However, the cutting process did influence
the residual stresses in the web, with high tensile stresses near the location of the cut. The perceived small influence of the cutting process on the flange stresses is likely due to the counteracting effects of the local heat introduction and the elastic rebound, which are expected to be of the same order of magnitude. Nevertheless, it is difficult to draw definitive conclusions
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(a)
(b)
Fig. 11. Evolution of the residual stresses in the flanges during the production process for geometries CS1&CS3 (a) and CS2 (b). The residual stresses in the parent section are given by PS. The stresses in the completed members (AW) are given at the web post (WP) and tee section (TS). For geometries CS1 and CS3 (a), the stresses in the separate halves after the cutting of the web (AC) are given as well for the tee section (TS) and the web post (WP).
from these measurements, since there was only a limited number of tested specimens for this case and no related results are available in literature. It could be further investigated by using finite element software, but since the focus of this work was on the residual stresses in the completed cellular or castellated members, this was not further examined. In the completed cellular or castellated members, the effect of the elastic rebound will only occur partially because both halves will be pushed together in a straight line before welding. Consequently, the equilibrating bending moment is delivered externally to the member halves. However, a rearrangement of residual stresses is still expected because of the normal equilibrium requirements.
3.2.4. Completed castellated or cellular members (AW) Due to the local heat introduction during welding, very high tensile stresses were expected at the weld. It is unclear to what extent the tensile zone width in the completed member will still be influenced by the previous effect of the cutting of the web. According to [26], the effect of welding at the same location as the cut almost completely relieves the already present residual stresses due to cutting, while according to [23] the tensile stress zone size will depend on both the cutting and welding process. The effect of the welding process on the residual stresses in the completed castellated sections CS1 and CS3 is clearly noticeable in Figs. 9 and 11. At the flange tips, a significant residual stress decrease of about 50 MPa is noticeable, while the residual stresses at the flange centres decrease as well. This increase in compressive flange stresses is caused by an increase of the web (tensile) residual stresses at the location of the weld and the cut, as expected. Taking into account the variation of the modulus of elasticity E and the error on the strain measurement, it is possible that the flange stress decrease due to the production process is less extreme (42 MPa). Nevertheless, the magnitude of the residual stress decrease at the flange tips remains significant. The additional effect of the cutting of the circular openings in CS2 can be seen in Figs. 10 and 11. The effect of the additional heat input close to the flanges is noticeable in the tee section, where the tensile residual stresses in the web are very high. These stresses are balanced by a large increase of compressive residual stresses in the flanges. At the web post, the residual stresses in the flanges decrease less drastically to the same level as for geometries CS1 and CS2. The measured residual stresses in the web at the tee section were very high (up to 371 MPa), even larger than the measured yield stress, which is theoretically impossible. This could be caused by the high assumed value of E: if the real Young’s mod-
ulus would only be 10% lower, a value of 334 MPa would be obtained, which is far more realistic. Other, but less likely explanations could be the hardening of the steel, three-dimensional stress fields close to the fillet between web and flange, or local deviations of the yield stress. The results for the completed geometries CS1 and CS3 show an increase of the compressive residual stresses in the flange because of the production process. The deviating production process of the CS2 geometry causes even higher compressive residual stresses at the flange. As a result, it is expected that the effect of residual stresses is more detrimental for the global buckling resistance of cellular or castellated members than it is for their parent sections.
4. Conclusions It is expected that the global buckling behaviour of cellular and castellated members is different than that of plain-webbed members, due to the effect of the modified geometry and the influence of the production process on the present imperfections. Regarding the latter effect, the largest influence is expected for the residual stresses. In this paper, it was examined to what extent the cellular and castellated member production processes modify the residual stresses present in these members. This was done by measuring the residual stresses in the parent sections and completed castellated members, as well as in the cut section halves. Additionally, the effect of a deviating production procedure for the cellular members was studied. The focus was on the flange residual stresses because the compressive residual stresses in the flanges will have a dominant detrimental effect on the global buckling resistance. The residual stresses in the completed castellated and cellular members are the most important, because these will determine the buckling resistance of these members. In the completed castellated members, the influence of the production process on the flange residual stresses could be seen clearly: the compressive residual flange stresses increased both at the web post and at the tee section. The modified residual stresses will have a detrimental effect on the castellated members’ stability. It is expected that the residual stresses in cellular members made according to the standard production procedure will correspond well to the values measured for the castellated members. The detrimental effect of the production process was even larger for the cellular members made according to the deviating production procedure. Because of the local heat input close to the
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D. Sonck et al. / Construction and Building Materials 54 (2014) 512–519 Table 3 Location of strain gages in flanges and in web (y and z are given in mm). Flanges CS1–CS3
y1 30
y2 15
y3 0
y4 15
y5 30
Web CS1 and CS2 PS AC and AW: TS AC and AW: WP
z1 48.6 78.9 78.9
z2 18.6 78.9 48.9
z3 0 – 30.3
z4 18.6 – 11.7
z5 48.6 – 11.7
z6 – 30.3
z7 – 48.9
z8 – 78.9
Web CS3 PS AC and AW: TS AC and AW: WP
z1 53.5 93.1 93.1
z2 .26.5 93.1 66.1
z3 0 – 39.6
z4 26.5 – 13.1
z5 53.5 – 13.1
z6 – – 39.6
z7 – – 66.1
z8 – – 93.1
flanges during the cutting of the circular openings in the completed castellated sections, the measured flange residual stresses at the tee section were totally in compression. At the web post, the effect of the supplementary cutting procedure was smaller: the residual stresses at the flanges corresponded well with the residual stresses measured in the castellated sections. However, care should be taken not to introduce local heat close to the flanges in the completed cellular or castellated members, as this could have dramatic consequences for the compressive residual stresses in the flanges and the corresponding global buckling resistance of the concerned members. The effect of the adversely modified residual flange stresses should be taken into account when calculating the resistance of cellular or castellated members. In future research, these results could be used to construct a valid finite element model to study the global buckling resistance of cellular and castellated members, based on which accurate expressions for the buckling resistance could be developed. Acknowledgement The authors would like to thank Huys-Liggers (Venlo, The Netherlands) for supplying the specimens used in the experiments. Appendix A The exact location of the strain gages, according to Fig. 12, is given in Table 3.
Fig. 12. Location of strain gages.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental investigation of residual stresses in steel cellular and castellated members Delphine Sonck ⇑, Rudy Van Impe, Jan Belis Department of Structural Engineering – LMO, Ghent University, Technologiepark-Zwijnaarde 904, 9052 Ghent, Belgium
h i g h l i g h t s Cellular or castellated members are fabricated from hot-rolled parent sections. Residual stresses lower the global buckling resistance of the parent sections. The production process influence was determined by measuring the residual stress. During the production process, the residual stresses become more detrimental.
a r t i c l e
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Article history: Received 26 August 2013 Received in revised form 29 November 2013 Accepted 16 December 2013 Available online 23 January 2014 Keywords: Residual stresses Cellular members Castellated members Hot-rolled I-members Imperfection Flexural buckling Lateral–torsional buckling
a b s t r a c t The global buckling resistance of hot-rolled steel I-section members is adversely influenced by the presence of residual stresses. It is expected that thermal effects during the production of cellular and castellated members will influence the already present stresses in the hot-rolled parent sections, but it is yet unknown to what extent. In this paper, the experimental investigation of the residual stresses in these members is described, and it is shown that the production process increases the already present compressive flange stresses, which will be detrimental for their buckling resistance. This effect will be even more pronounced for deviating production procedures. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Cellular or castellated members are I-section members with circular or hexagonal web openings regularly spaced along the length of the member. Usually, they are manufactured starting from steel hot-rolled I-section members of which the web is thermally cut according to a certain pattern, after which the obtained halves are shifted and rewelded (Fig. 1). Variations in the cutting pattern and the properties of the top and bottom halves of the beam result in a large variety of final member geometries, in which tapered beams, different web opening shapes or asymmetric beams are possible. The main advantage of cellular or castellated members compared to normal I-section members is their increased strong-axis bending resistance. Furthermore, service ducts can be guided
⇑ Corresponding author. Tel.: +32 9 2645469. E-mail addresses: [email protected] (D. Sonck), Rudy.VanImpe@ UGent.be (R. Van Impe), [email protected] (J. Belis). 0950-0618/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2013.12.045
through the web openings instead of under the member, thus diminishing the necessary total story height. Additionally, they can also be used out of aesthetic considerations because of their lighter appearance. The members are mainly used for applications in which they are loaded in bending, both in steel and steel– concrete construction. However, they are also increasingly used for columns and beam-columns, where the column is subjected to both bending and compression. Clearly the presence of the web openings will influence the failure behaviour of cellular or castellated members [1]. For instance, new localized failure modes can arise, such as Vierendeel bending around the web openings or local buckling of the web surrounding the openings. Specific rules for these failure modes are currently being developed and optimized [2–8]. However, the already existing failure modes for I-section members will also be modified, because of the change in geometry and the influence of the production process on imperfections such as geometric imperfections and residual stresses. Examples of this are the global instability failure modes for members loaded in compression and/or bending, such as
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Fig. 1. Standard fabrication method of castellated and cellular members starting from a plain-webbed parent section.
flexural buckling or lateral–torsional buckling. Unfortunately, the existing research for these global instability modes is incomplete, conflicting or lacking altogether [9–11]. An important aspect of the global instability behaviour of cellular and castellated members that has not been investigated yet is the influence of residual stresses. Residual stresses are internal stresses which can exist in a member not subjected to external loads. Hence, residual stresses are always in static equilibrium. In hot-rolled I-section members, thermal residual stresses originate during the cooling after the hot-rolling process because of the non-uniform cooling and corresponding thermal contraction, coupled with a temperature-dependent yield stress. Typically, the flange tips will be in compression and the flange centres in tension, while the sign and variation of the residual stresses in the web varies depending on the cooling parameters and cross-section geometry [12–17]. Examples of typical thermal residual stress shapes are shown in Fig. 2 [17,18]. If the straightness of the beams after cooling is not sufficient, the beams will undergo a cold-straightening process which redistributes the residual stresses in the flanges [19,20]. As a result, the possible residual stress patterns in I-section members are very diverse. The influence of residual stresses on the global buckling failure of I-section members without web openings has been studied extensively for the cases of flexural buckling [14,15] and lateral– torsional buckling [21], which are the most important global failure modes for I-section members. It was shown that the residual stresses have a detrimental effect on the global buckling resistance of the I-section members, caused by the compressive residual stresses at the flange tips. Due to these stresses, the onset of yielding will occur quicker at the flange tips, increasing the members’ flexibility and reducing the corresponding buckling resistance. Furthermore, it was shown that the redistribution of the flange stresses due to cold-straightening is always advantageous for the failure load [16,19,20,22]. Therefore, it was decided not to take this into account in the proposed standard residual stress patterns and to consider only the more detrimental thermal residual stress pattern in finite element calculations to determine the buckling resistance. Likewise, only non-straightened members were used in the flexural buckling experiments to determine the buckling resistance of columns [23]. During the cutting and welding processes in the production of cellular or castellated members, heat is introduced at the cutting
(a)
and welding locations, which will influence the already present residual stresses. At the locally heated zone, very high tensile residual stresses (up to the material’s yield stress) will be present, balanced by compressive (and possibly also tensile) stresses farther away from the location of heat introduction [15,19,23–28]. Typical schematized residual stress distributions for plates cut at one side and plates welded in their middle are depicted in Fig. 3. As a result, it is very well possible that the production process increases the magnitude of the compressive residual stresses in the flanges, hence decreasing the global buckling failure load. Nevertheless, the change in residual stresses of cellular and castellated members during their production process has not been investigated yet and it is currently not known how significant the possible detrimental effect on the members’ stability will be. In this paper, the effect of the production process of cellular and castellated beams on the residual stresses is investigated by measuring the residual stresses in a series of castellated and cellular members. Measurements were done both for the parent sections and the resulting castellated and cellular members. By comparing the measured stresses before, during, and after production, the effect of the production procedure could be studied. In this paper, tensile stresses will be taken as positive stresses and compressive stresses as negative. 2. Residual stress measurement method and specimens In this section, an overview will be given of the used measurement method and the specimens in which the residual stresses were measured. All measurements were done at the Laboratory for Research on Structural Models (LMO, Ghent University). 2.1. Measurement method The residual stresses were measured using the sectioning method, which is a destructive relaxation method. The longitudinal residual stresses in each segment can be calculated using the strain difference before and after the relaxation of each segment. The relaxation of each segment is accomplished by the sectioning of the member. First, the member is cut transversally at the location of measurement, after which a series of longitudinal cuts is made to separate all segments in which the strains are measured
(b)
Fig. 2. Residual stress pattern in hot-rolled I-section members: (a) according to ECCS [18]; (b) according to Young [17].
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(a)
(b)
Fig. 3. Schematized residual stress pattern in: (a) plate welded in middle; (b) plate cut at one end.
were permanently damaged during the measurements: from the total of 360 used strain gages, 31 were found faulty. The measured strains in these gages (if any) were not included in the results. 2.2. Used specimens
Fig. 4. Overview of the sectioning method.
(Fig. 4). Because of its straightforwardness, this method is the primary method for the longitudinal residual stress measurement in steel I-section members, having been extensively used in the past as well as nowadays [12–15,17,20,22,24–29]. At each measurement location, the residual stress magnitude rres was calculated according to Eq. (1) using the measured relaxation strains emeas and the modulus of elasticity E. It was assumed that the specimens behaved elastically during the measurements, that the transverse residual stresses could be neglected, and that the thermal influence of the cutting process on the residual stresses was negligible.
rres ¼ E emeas
ð1Þ
The residual stresses were expected to vary along the length of the non-uniform castellated and cellular members. To study this effect, the residual stresses in these members were measured between the openings (web post in Fig. 1) and at the centre of an opening (tee section in Fig. 1). Adhesively bonded electrical strain gages were used to cope with the necessary short gage length. Another advantage of using electrical gages was that the strain variation during the measurement (and cutting) process could be easily monitored continuously. The resistance changes corresponding with the strain variations in the strain gages were measured using a Wheatstone bridge. Temperature variations during the sectioning process were accounted for by using self-temperature-compensated strain gages specifically designed for mild steel. The error on the strain measurement is estimated to be ±1.5%. The cutting process was executed with an electrical band saw, combined with a handsaw for some of the transverse cuts. Cutting oil was used to limit local heating of the specimens. A protective coating was used to protect the strain gages from this oil. During the cutting, the measured strains were continuously monitored to be sure that there was no malfunctioning of the strain gages due to damage suffered during the multiple manipulations throughout the sectioning process. However, some strain gages
Four castellated and two cellular members were made starting from six IPE160 parent sections: three geometries were used and two members were made for each geometry. Geometries CS1 and CS3 had hexagonal openings, while the CS2 beams had circular openings (Fig. 5). The steel grade of the members was S275, with a nominal yield stress of 275 MPa. Tensile tests to determine the yield stress fy were executed on specimens from the flanges and the web of each member (Table 1). The Young’s modulus E could also be derived from the tensile test measurements. Unfortunately, some of the obtained values for E were too aberrant from the mean values given in literature [30], probably due to a faulty displacement measurement during the test (these values are not included in Table 1). As a result, it was chosen not to use the measured values of E for the residual stress calculations, but to use E = 210 GPa as a safe mean value. Taking the variability of the values of the Young’s modulus E into account, the possible error on the residual stress measurements increases. This can be illustrated for the flange stresses, using values of Emean ± 2 Est. dev., based on the measured values of E in the flanges. If the real value of E would be 179 GPa instead of the used 210 GPa, the calculated residual stress is 15% larger than its real value. On the other hand, if E = 223 GPa, the calculated residual stress is 6% smaller than the real residual stress value. Six IPE160 beams of 12 m long were used as the parent section. Before the production of the castellated and cellular members, a specimen of 1 m long was cut from each parent section beam, to determine the original residual stress pattern in the parent sections. Geometries CS1 and CS3 were made following the standard
Table 1 Yield stresses obtained from the tensile tests, comparison with literature [30]. Yield stress, fy [MPa]
Web Flanges Literature
Young’s modulus, E [GPa]
# Samples
fy,mean
fy,st.
8 12 –
332 346 327.93
7 5 18.96
dev.
# Samples
Emean
Est.
6 11 –
195 201 205.47
12 11 13.18
Fig. 5. Dimensions [mm] of the parent section PS and the castellated and cellular member geometries CS .
dev.
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Fig. 6. Production process: (a) cutting of the web; (b) welding of the castellated members; (c) additional cutting of the circular openings for the CS2 geometries.
procedure depicted in Figs. 1 and 6a and b. First, the parent section webs were cut according to the corresponding pattern for hexagonal openings using an oxyfuel cutting process. After the cutting of the web, both halves of the beam were shifted and welded together again using a semiautomatic MAG welding process. A but joint existing of two weld passes – one on each side of the web – was used. For each of both geometries, a section was left unwelded so that the influence of the cutting process alone on the residual stresses could be studied in the obtained castellated member halves. The CS2 geometries had circular openings. Normally, cellular members are fabricated following a similar procedure as for castellated members, with two cut lines in the web instead of one to obtain the circular opening shapes (Fig. 1). However, the production of the two CS2 members deviated from this procedure: the members were made by cutting circular openings around the hexagonal openings of two completed castellated members with a CS1 geometry (Fig. 6c). Thus, the effect of deviating production procedures on the residual stresses could be examined as well. The heat input using this deviating procedure was larger than for the standard production procedure of CS1 and CS3 because the cutting process had to be restarted for each separate web opening. The strains were measured at five locations in each flange. In the web, five strain gages were used for the parent sections, while two gages were used at the tee section and eight at the web post for the cellular or castellated members. It was expected that measurements on one side of the flanges or the web would suffice, since it had been shown that the through-thickness stress variations in thin-walled hot-rolled members such as the considered specimens is limited [12,13]. Consequently, all measurements were done on the outer side of the flanges and on the same side of the web. The exact location of the strain gages is given in Appendix A. An overview of the specimens in which the residual stresses were measured is given in Table 2. In total, the residual stresses were measured in six parent section specimens (PS), two unwelded castellated member specimens (AC) and seven castellated or cellular member specimens (AW). For both the AC and AW specimen types, measurements were made at two locations along the
length: the residual stresses were determined between two openings (web post WP) and at the centre of an opening (tee section TS). The measurements in the unwelded castellated members specimens occurred for both the top and bottom halves of the cut IPE160 section. All specimens were taken from the same end of the members. The length of each specimen was chosen such that the distance between the measurement locations and the specimen edge was at least twice the height of the specimen. Thus, possible disturbances of the residual stresses by edge effects were avoided. The remainder of the castellated and cellular members is being used for buckling experiments which are beyond the scope of this contribution. 3. Measurement results and discussion 3.1. Measurement results The results of the residual stress measurements in the parent section are shown in Fig. 7. The effect of the cutting of the parent sections of the CS1 and CS3 geometries can be seen in Fig. 8, both for the tee section and the web post. The final residual stress distribution in the geometries CS1 and CS3 is shown in Fig. 9, while the residual stress distribution for CS2 is shown in Fig. 10. The measurements for geometries CS1 and CS3 are shown together, since they were found to be very similar. In Figs. 7–9, the measured values of the residual stresses are shown for each specimen, together with the corresponding leastsquare fit (LSF) curves for the residual stresses in the flanges. The LSF curves were obtained by mirroring the results about the horizontal and vertical symmetry axes of the cross-section, after which these values were fitted to a linear function. This function shape is based on the perceived variation of the residual stresses across the flanges. Since the compressive residual flange stresses have a dominant detrimental influence on the global buckling resistance, an overview of the variation of the flange stresses during the production process is depicted in Fig. 11. Here, the least-square fit curves of the measured residual stresses in the flanges are shown. 3.2. Discussion of residual stress measurements
Table 2 An overview of the test specimens. Measurements were done in three different sections: parent section (PS), sections after cutting (AC) and after welding (AW). In the latter two, measurement occurred at the web post between two openings (WP) and at the tee section at an opening (TS). Member name
# Locations parent section (PS)
# Locations after cutting (AC)
# Locations after welding (AW)
CS1L1 CS1L2 CS2L1 CS2L2 CS3L1 CS3L2
PS
WP
TS
WP
TS
1 1 1 1 1 1
2 0.5 0 0 0 2 0.5 0
2 0.5 0 0 0 2 0.5 0
1 1 2 1 1 1
1 1 2 1 1 1
Total
6
2
2
7
7
3.2.1. Influence of cold-straightening It was expected that the plastic deformation corresponding with the cold-straightening of a member around its weak axis is perceivable through antisymmetric residual stress deviations in the flanges. In the parent sections (Fig. 7), no influence of the cold-straightening of the beam was observed in the measured residual stresses in the flanges. However, in the flanges of the AC and AW specimens, the influence of cold straightening on the residual flange stresses is visible (Figs. 8–10). 3.2.2. Parent sections (PS) The measured residual stresses in the parent section (Fig. 7) are consistent with earlier results from literature and lie between the
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(a)
(b)
Fig. 7. Measured residual stresses in the parent section PS (a); comparison of the measured PS residual stresses with results from literature (b).
(a)
(b)
Fig. 8. Measured residual stresses in CS1 and CS3 in both halves after the cutting of the web during production: (a) in the web post; (b) in the tee section.
residual stress patterns proposed by Young and the ECCS [17,18], shown in Fig. 7. Furthermore, it can be seen that the measured residual stresses were very similar for the six parent section specimens, suggesting that all parent sections came from the same batch. 3.2.3. Member halves after cutting of the parent sections (AC) In Figs. 8 and 11, the residual stresses in the parent section halves obtained after the oxycutting of the web are depicted. It
was expected that this cutting of the parent sections would have a dual influence on the stresses in the obtained halves. Firstly, the thermal influence of the cutting process will induce tensile stresses at the cut, balanced by both compressive and tensile stresses further away from the cut. Secondly, an elastic rebound of the isolated halve of the member will occur when the forces acting on it by the other halve are removed. For the considered specimens, the elastic rearrangement of the residual stresses due to the elastic rebound was expected to increase the compressive flange stresses.
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(b)
Fig. 9. Measured residual stresses in completed CS1 and CS3: (a) in the web post; (b) in the tee section.
(a)
(b)
Fig. 10. Measured residual stresses in completed CS2: (a) in the web post; (b) in the tee section.
However, this compressive stress increase was expected to be counteracted by the increase in tensile flange stresses due to thermal effects. The total influence of the oxycutting process on the flange residual stresses in the beam halves was seen to be rather limited (Figs. 8 and 11). However, the cutting process did influence
the residual stresses in the web, with high tensile stresses near the location of the cut. The perceived small influence of the cutting process on the flange stresses is likely due to the counteracting effects of the local heat introduction and the elastic rebound, which are expected to be of the same order of magnitude. Nevertheless, it is difficult to draw definitive conclusions
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(a)
(b)
Fig. 11. Evolution of the residual stresses in the flanges during the production process for geometries CS1&CS3 (a) and CS2 (b). The residual stresses in the parent section are given by PS. The stresses in the completed members (AW) are given at the web post (WP) and tee section (TS). For geometries CS1 and CS3 (a), the stresses in the separate halves after the cutting of the web (AC) are given as well for the tee section (TS) and the web post (WP).
from these measurements, since there was only a limited number of tested specimens for this case and no related results are available in literature. It could be further investigated by using finite element software, but since the focus of this work was on the residual stresses in the completed cellular or castellated members, this was not further examined. In the completed cellular or castellated members, the effect of the elastic rebound will only occur partially because both halves will be pushed together in a straight line before welding. Consequently, the equilibrating bending moment is delivered externally to the member halves. However, a rearrangement of residual stresses is still expected because of the normal equilibrium requirements.
3.2.4. Completed castellated or cellular members (AW) Due to the local heat introduction during welding, very high tensile stresses were expected at the weld. It is unclear to what extent the tensile zone width in the completed member will still be influenced by the previous effect of the cutting of the web. According to [26], the effect of welding at the same location as the cut almost completely relieves the already present residual stresses due to cutting, while according to [23] the tensile stress zone size will depend on both the cutting and welding process. The effect of the welding process on the residual stresses in the completed castellated sections CS1 and CS3 is clearly noticeable in Figs. 9 and 11. At the flange tips, a significant residual stress decrease of about 50 MPa is noticeable, while the residual stresses at the flange centres decrease as well. This increase in compressive flange stresses is caused by an increase of the web (tensile) residual stresses at the location of the weld and the cut, as expected. Taking into account the variation of the modulus of elasticity E and the error on the strain measurement, it is possible that the flange stress decrease due to the production process is less extreme (42 MPa). Nevertheless, the magnitude of the residual stress decrease at the flange tips remains significant. The additional effect of the cutting of the circular openings in CS2 can be seen in Figs. 10 and 11. The effect of the additional heat input close to the flanges is noticeable in the tee section, where the tensile residual stresses in the web are very high. These stresses are balanced by a large increase of compressive residual stresses in the flanges. At the web post, the residual stresses in the flanges decrease less drastically to the same level as for geometries CS1 and CS2. The measured residual stresses in the web at the tee section were very high (up to 371 MPa), even larger than the measured yield stress, which is theoretically impossible. This could be caused by the high assumed value of E: if the real Young’s mod-
ulus would only be 10% lower, a value of 334 MPa would be obtained, which is far more realistic. Other, but less likely explanations could be the hardening of the steel, three-dimensional stress fields close to the fillet between web and flange, or local deviations of the yield stress. The results for the completed geometries CS1 and CS3 show an increase of the compressive residual stresses in the flange because of the production process. The deviating production process of the CS2 geometry causes even higher compressive residual stresses at the flange. As a result, it is expected that the effect of residual stresses is more detrimental for the global buckling resistance of cellular or castellated members than it is for their parent sections.
4. Conclusions It is expected that the global buckling behaviour of cellular and castellated members is different than that of plain-webbed members, due to the effect of the modified geometry and the influence of the production process on the present imperfections. Regarding the latter effect, the largest influence is expected for the residual stresses. In this paper, it was examined to what extent the cellular and castellated member production processes modify the residual stresses present in these members. This was done by measuring the residual stresses in the parent sections and completed castellated members, as well as in the cut section halves. Additionally, the effect of a deviating production procedure for the cellular members was studied. The focus was on the flange residual stresses because the compressive residual stresses in the flanges will have a dominant detrimental effect on the global buckling resistance. The residual stresses in the completed castellated and cellular members are the most important, because these will determine the buckling resistance of these members. In the completed castellated members, the influence of the production process on the flange residual stresses could be seen clearly: the compressive residual flange stresses increased both at the web post and at the tee section. The modified residual stresses will have a detrimental effect on the castellated members’ stability. It is expected that the residual stresses in cellular members made according to the standard production procedure will correspond well to the values measured for the castellated members. The detrimental effect of the production process was even larger for the cellular members made according to the deviating production procedure. Because of the local heat input close to the
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D. Sonck et al. / Construction and Building Materials 54 (2014) 512–519 Table 3 Location of strain gages in flanges and in web (y and z are given in mm). Flanges CS1–CS3
y1 30
y2 15
y3 0
y4 15
y5 30
Web CS1 and CS2 PS AC and AW: TS AC and AW: WP
z1 48.6 78.9 78.9
z2 18.6 78.9 48.9
z3 0 – 30.3
z4 18.6 – 11.7
z5 48.6 – 11.7
z6 – 30.3
z7 – 48.9
z8 – 78.9
Web CS3 PS AC and AW: TS AC and AW: WP
z1 53.5 93.1 93.1
z2 .26.5 93.1 66.1
z3 0 – 39.6
z4 26.5 – 13.1
z5 53.5 – 13.1
z6 – – 39.6
z7 – – 66.1
z8 – – 93.1
flanges during the cutting of the circular openings in the completed castellated sections, the measured flange residual stresses at the tee section were totally in compression. At the web post, the effect of the supplementary cutting procedure was smaller: the residual stresses at the flanges corresponded well with the residual stresses measured in the castellated sections. However, care should be taken not to introduce local heat close to the flanges in the completed cellular or castellated members, as this could have dramatic consequences for the compressive residual stresses in the flanges and the corresponding global buckling resistance of the concerned members. The effect of the adversely modified residual flange stresses should be taken into account when calculating the resistance of cellular or castellated members. In future research, these results could be used to construct a valid finite element model to study the global buckling resistance of cellular and castellated members, based on which accurate expressions for the buckling resistance could be developed. Acknowledgement The authors would like to thank Huys-Liggers (Venlo, The Netherlands) for supplying the specimens used in the experiments. Appendix A The exact location of the strain gages, according to Fig. 12, is given in Table 3.
Fig. 12. Location of strain gages.
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